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The Actuary The magazine of the Institute & Faculty of Actuaries

Arbitrage and volatility

Chatterjee and Knowles’s second article on arbitrage-free pricing in the July issue discusses weaknesses of ‘implied market volatility’, highlighting the fact that it is volatile and differs from historic volatility, sometimes significantly. These views differ from mine for the following reasons:

  • 1 ‘Implied market volatility’ is a misleading term. It is famously ‘the wrong parameter, in the wrong model, to get the right price’.
  • 2 Explaining the difference between ‘implied market volatility’ and historic volatility (figure 3) as ‘profit margins’ is also misleading. See Sheldon and Smith (2004) ¶6.4.3 for a list of reasons other than profit for this difference. [Sheldon, TJ and Smith, AD (2004): ‘Market-consistent valuation of life assurance business’, British Actuarial Journal (to appear)”
  • 3 Market prices of options move up and down, in the same way that asset index levels and yield curves move up and down. For a life insurer running an asset liability mismatch by selling unhedged financial options, this is just another market risk to the balance sheet that should be monitored and managed. Some life insurers are more exposed to this risk than others.

The article ends by encouraging the use of the average of observed implied market volatilities in a long-term valuation, stating that ‘the result might be acceptable’. To whom? Owing to the above, I think this has even less merit than the now discredited use of smoothed asset index levels or smoothed yield curves when carrying out prospective valuations of liabilities.